Leonid Hrabovsky (born 1935) is one of the pioneers whose works indicated the opening of the modernist era in Ukrainian music of the late 20 century.

At the end of the 1950^th, like many others, he started out within the familiar idiom of the late Romanticism – early post-Impressionism with folkloristic roots (Four Ukrainian Songs, 1959), but soon turned to post-tonal techniques that included free dissonant style (following Prokofiev/Bartok/Hindemith of the early 1920s) (Symphonic Frescoes, 1961), then to 12-tone procedures (Four Two-Part Inventions and Five Character Pieces for piano, 1962). Shortly after that, Hrabovsky started the series of compositions based on mixtures of isolated, contrasting atonal and modal pitch sequences, irregular sonic elements including approximately notated (clusters and extremely rapid passages), non-pitched noises, partially aleatoric rhythms, and free space notation.  It includes such compositions as Trio for Piano, Violin & Double Bass, Microstructures for solo oboe, From Japanese Haiku for Tenor, Flute Piccolo, Bassoon & Xylophone, Pastels for Female Voice, Violin, Viola, Cello & Double Bass to the poetry by Pavlo Tychyna, and Constants for 4 Pianos, 4 Percussion Groups & Solo Violin (all 1964). Two more short works in the same style, Rilke Epitaph for Soprano, Harp, Celesta, Guitar & Tubular Bells (on the text from the Rilke’s grave inscription), and Marginalien zu Heissenbuettel for Reciter, 2 Trumpets, 2 Trombones and Percussion on three short poems of German avant-garde poet Helmut Heissenbuettel, were composed in the next two years (1965-66).

In the same 1964, Hrabovsky began preparations to the composition of the melodrama La Mer to the texts of Saint-John Perse, for narrator, mixed choir, and large symphony orchestra including big percussion section, organ and two pianos. As the base for his 20-minutes work H. selected a special row of 11 perfect fifths (a0 – d7) with its various transformations, a number of them sounding mellow consonant ones – on one hand, but also the chromatic scale as one else result of these transformations which might serve the “legal basis” for including clusters in the orchestral web, on other hand.  Since the whole preparation included the process of selection of the fragments from the vast, almost 190 pages long, poem & its translation into the Ukrainian language, La Mer had seen its completion much later, in the summer of 1970.

While influenced by the music of new Polish school (Krzysztof Penderecki, Witold Lutoslawski, Henryk Mikołaj Górecki and particularly Kazimierz Serocki (the latter created one of the most consistent system of partial aleatoric rhythm notation)) in his composition practices during that period, Hrabovsky started to feel a growing dissatisfaction with the patch-like coloristic approach to the composition concept. Finally, he haд arrived at the conclusion that, like in painting, the accent on color patch with the diminished role of contour, of drawing may – and do – limit the viability of his music. Looking back at the 12-tone dogma in its classical implementation, Hrabovsky saw its potential leading to monotony and to a kind of discoloration as the outcome of steadily equal presence of all 12 pitches in the music fabric. Especially harmful role he attributed to highly popular use of all-interval series cherished by numerous composers at the peak-time of the dodecaphony.

In search of the way out, Hrabovsky reflected on remarkable figures of the time like Olivier Messiaen and his disciple, Iannis Xenakis. He anticipated that the modal principle based on diatonic origins might be more fruitful than the total chromaticism, and music of these masters was seen as persuading path in that sense. At the same time, Hrabovsky ran into Polish almanac Res facta with an article on probability and methods of its usage in fine arts. As a result, he initiated construction of all possible 7-pitch scales using all flats, naturals and sharps which gave him 365 such scales subsequently chained into 104 large non-octaviated tone rows covering the whole piano pitch space from a0 to c8. (Some theorists named it meta-series).

Then the question arose: how and where to start with that entire huge ocean of possibilities?

Like in the Second Viennese school practice of breaking 12-tone series into hexachords, tetrachords and trichords, the logical idea was to cut out segments of various lengths from these rows, and turn them into vertical, diagonal or linear building blocks of music texture. The next question was: what principle has to be set to determine starting and ending points, and the lengths?

Hrabovsky found the answer in the concept of bijection. In math, bijection is a function between the elements of two sets where each element of one set is paired with exactly one element of the other set. The concept was applied to the correspondence between the random number and the smallest musical unit – a separate note, in this case the start and end pitches. Thus, the probability was introduced and incorporated into the compositional process that has to produce unambiguously notated scores. Carefully determined domains of random numbers continuum were established as ruling laws of how the music texture unfolds, allowing both sharp contrasts and step-by-step evolutionary processes that slow or at various speeds change these or other characteristic features of developing sonic constellations.

The very first project experimenting with this new method was the Homoeomorphies I-III for 1 and 2 Pianos (1968-69), followed by Homoeomorphy IV for Large Orchestra (1970). In all these compositions, Hrabovsky used mostly single rhythm ideas – equal flow of 16ths (I), some proportional space notation with single units of 1 to 60 lengths (II), equal flow of 3 different durations – 32ths, dotted 16ths and double-dotted 8ths (1, 3 and 7 lengths, III), and superpositions of vertical tone blocks built in 3 sections of orchestra –winds, pitched percussion and strings (density 1 to 49 pitches) with respective, highly variable lengths from few 16ths to several whole notes – tied, dotted & double or triple-dotted, or expanded otherwise (IV).

In 1972 Hrabovsky developed the list of 2042 rhythmic patterns (based on 1/16 duration) using simple logical deduction way. There were three large sections created:  units, tied in various combinations (from triplets up to undecaplets), syncopated units (including number of diverse direct and Lombard rhythm from triplets to nonuplets), and broken units (several 16ths within the group that are broken into 2/32 or 3/32 – also from triplets to nonuplets).

That development has created a possibility of making hybrid figures by merging two figures of equal length but of different sections, into one. It is still a problem even at the computer level of Lisp programming of today, as to how to break this merger process into comprehensive single steps. Back then, Hrabovsky did it by hand in “For Elissa” on few selected figures’ pairs.

The ways of development of the whole work from initial materials in Hrabovsky’s method might be generalized in a notion of total variability and preferable asymmetry. Hrabovsky states as his general principle - the non-repetition – accordingly to the maxim of Arnold Schoenberg – and as the subordinate one, partial or reduced repetition – in well known of 12-tone basic series forms Original, Retrograde, Inversion and Retrograde of Inversion, further – in applying Gothic Talea and Color technique, and evolving ostinato in form of steady expanding a sequence from 2 to 3 to 5 to 8 etc. elements (Fibonaccization) or the opposite process of reducing it (de-Fibonaccization). The Fibonacci series might be substituted or transformed by adding to its members a constant coefficient. The one and the same rhythm line might be repeated with different pitch sequence, or vice versa.

Additionally, the computer function or even a function in Microsoft Word may make instant replacement in a rhythm – all 8-ths by 16-ths, 4-ths by 8-ths, 2^nds by 4ths etc., or more paradoxically – to turn 16ths into 4ths and vice-versa but preserving 8ths – that completely turns one rhythm picture into quite opposite, literally - positive into negative. In pre-computer era, that operation, now instant, might take hours of petty handwork. Thus, it seems that the old music theory and practice, while knowing of simplest double increase and decrease of a fugue or canon theme, just could not come to this incomparably more exquisite technique of theme transformation.

The base of the Hrabovsky’s Method of Algorithmic Composition was much later upgraded to a computer-assisted method, creating one of the most needed possibility to speed up the slow, hand-picking routine processes

“Für Elise” (“For Elissa”) piano piece (1988) has been the first outcome of implementing this imposing vocabulary including both 104 pitch-chains and 2041 rhythm figures.

“Temnere mortem” for a cappella chamber chorus (1991) continued the trend, this time with rhythm language reduced to septuplets of 4ths with the aim to create an allusion to ancient Orthodox chants.

In parallel, two scores for singer and chamber ensemble were written outside of algorithmic method and become a continuation of 1960-s mixed technique – “Kogda” for Mezzo-Soprano, Violin, Clarinet, Piano and additional Percussion (1987) and “And It Will Be” for same ensemble with a pianist also playing on CASIO-100 synthesizer (1993). Several sections of the symphonic poem for three orchestral groups “Vorzel” (1992) were composed by the algorithmic method application.

In 2010s the implementation of some 50 both ready and newly written functions of computer programming language Common Lisp allowed Hrabovsky not only to greatly increase the composing productivity, but also let him expand his pitch-chain repertory from one early 104-set by adding 21 new ones, also with 104 pitch-chain in each. They all are multi-unit sets of endlessly variable sequences of intervals: from 1-2-1-2 (mix of minor and major seconds) through 2-3, 3-4, 1-2-3, 2-3-4 etc., up to 1-2-3-4-5-6 –  obtained by mixing together different quantities of each interval in various proportions. This upgrading step brought into Hrabovsky’s composing practice even more finely differentiated nuances of consonances & dissonances proportions in harmony and most variable intervallic content in linear domain.

Also, by simple operation of substituting values in rhythm pattern lists, the original 2041-figure set was quadrupled, and became a 8164-figure set, including now 8^th-, 4^th- and 2^nd-based sections. Free mixing of figures picked-up from different groups constitutes limitless rhythm vocabulary for usage in coming up compositions.

In addition, some simple Common Lisp functions gave the composer yet another possibility of building rhythms by freely mixing and re-mixing many times selected groups of elementary values (for example, 5 eights, 7 dotted eights, 9 sixteenths and 3 quarters put in a row and shuffled like cards) thus obtaining most capricious flow of their highly changeable and volatile combinations.

With his Computer Assisted Algorithmic Method, Hrabovsky resumed composing of essential instrumental music and added, in recent years, 5 new works to his list:

   12 Two-Part Inventions for Harpsichord (2016),

“Tetragon” – Symphony-Capriccio for 4 Guitars & Strings (2017),

“ARRY” for String Orchestra (2018),

“Credo” for Brass, Strings, Percussion, Piccolo Flute & Four-Hands Piano

“EQVIN” for Violin & Piano (both 2019)